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Matthew 10:14
If anyone will not welcome you or listen to your words, leave that home or town and shake the dust off your feet.
Matthew 10:13-15 (in Context) Matthew 10 (Whole Chapter)

However, when you said; "turn your back on the non believer", I do not see that.

In 1 Thessalonians we are told to pray without ceasing. In all things at all times we should be cognizant of our relationship to God.
http://biblegateway.com/passage/?search=1%20Thessalonians%205:17&version...